The present invention relates to a system and method to measure gas flow using upstream and downstream pressure measurements, and in particular to measurement of flows related to internal combustion engine operation.
Determining compressible gas flow from pressure measurements is commonly performed using the known adiabatic orifice compressible flow equation shown in the following equation, referred to herein as a true flow function.                               m          .                =                              A            o                    ⁢                                                    2                ⁢                k                                            k                -                1                                              ⁢                                                    M                ⁢                                  xe2x80x83                                ⁢                W                                            RT                1                                              ⁢                      p            1                    ⁢                                                    r                                  2                  k                                            -                              r                                                      k                    +                    1                                    k                                                                                        equation        ⁢                  xe2x80x83                ⁢        1                                r        =                  {                                                                                          p                    2                                                        p                    1                                                                                                                                          p                      2                                                              p                      1                                                         greater than                                                             (                                              2                                                  k                          +                          1                                                                    )                                                              k                                              k                        -                        1                                                                                                                                                                                      (                                          2                                              k                        +                        1                                                              )                                                        k                                          k                      -                      1                                                                                                  otherwise                                                                        xe2x80x83            
where,   m  .
is mass flow rate, Ao is orifice area, MW is molecular weight of gas flowing through the orifice, k is the ratio of specific heats, p2 is downstream pressure, p1 is upstream pressure and T1 is upstream temperature. The variable, r, can take on two values depending on the ratio of downstream to upstream pressure. When the ratio is greater than a certain value, flow is said to be subsonic and the upper equation is followed. When the ratio is less than a certain value, flow is said to be sonic, or choked, and the lower equation is followed.
However, due to complex exponents and corresponding difficulties in cost effective implementation of the above equation in digital computers that run at high speed, approximations to the adiabatic orifice compressible flow equation are commonly sought.
One approximation to equation 1 is given in terms of differential pressure between upstream and downstream conditions and downstream pressure. The known equation is given as:       m    .    =            A      o        ⁢          2        ⁢                            M          ⁢                      xe2x80x83                    ⁢          W                          RT          1                      ⁢                                        a            ⁡                          (                              Δ                ⁢                                  xe2x80x83                                ⁢                p                            )                                ⁢                      p            2                          -                              b            ⁡                          (                              Δ                ⁢                                  xe2x80x83                                ⁢                p                            )                                2                    
where, a is given as 1 and b is given as   (            1.5      k        -    1    )
and xcex94p=p1xe2x88x92p2. Such a method is described by Holman in, Experimental Methods for Engineers, 2nd Edition, 1966.
The inventor herein has recognized several disadvantages with the above approximation. In particular, the above approximation has a limited region of applicability as stated by Holman. In other words, the above approximation only resembles the true flow function in a limited operation region when using the fixed values of a and b stated by Holman. Another disadvantage is that the prior art approximation is invalid during subsonic operation and no corresponding transition point is given in terms of variables xcex94p and p2. Another disadvantage is that values of a and b stated by Holman are only applicable for small area ratios between orifice area and pipe area.
An object of the invention claimed herein is to provide a flow measurement method for measuring compressible flow using an approximation that is useful over all operating conditions and used in conjunction with various gas types.
The above object is achieved, and problems of prior approaches overcome, by A method for determining a flow of a compressible gas through an orifice, the method comprising: determining first and second constants based on an error between a flow approximation and a true flow function, wherein said flow approximation is based on said first constant, said second constant, an upstream pressure variable, a downstream pressure variable, and a differential pressure variable; calculating an actual differential pressure between an actual upstream pressure and an actual downstream pressure; and calculating a compressible gas flow based on said actual upstream pressure, said actual downstream pressure, said actual differential pressure, and said first and second constants using said flow approximation.
By using an approximation according to the present invention, not only can extremely accurate approximations be achieved, but the approximations are valid over all pressure conditions. In other words, the approximation of this form can be used in pressure ranges under which the prior art produced inaccurate results and therefore in pressure ranges in which the prior art discouraged approximations. In fact, the approximation according to the present invention achieves higher accuracy than the prior art in all pressure ranges, including those ranges in which the prior art approach is taught to be useful.
An advantage of the above aspect of the invention is that more accurate flow measurement is obtained across all pressure ranges.
Another advantage of the above aspect of the invention is that the more efficient real time software is obtained.
Other objects, features and advantages of the present invention will be readily appreciated by the reader of this specification.